{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:5YY5DO4MJ7YDYGGWSZYLDMG2VG","short_pith_number":"pith:5YY5DO4M","canonical_record":{"source":{"id":"2402.04840","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-02-07T13:41:45Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"264c1986df7219064932c1e76e24282d87f39f44e772465057dc71da6573b9c2","abstract_canon_sha256":"9a296e098d11eb0e62f522f72be383fb807e9ab451fe5c16e7b4587e1459569e"},"schema_version":"1.0"},"canonical_sha256":"ee31d1bb8c4ff03c18d69670b1b0daa9bc1731cc07328b4ea70e625076b16d94","source":{"kind":"arxiv","id":"2402.04840","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.04840","created_at":"2026-07-05T10:24:20Z"},{"alias_kind":"arxiv_version","alias_value":"2402.04840v3","created_at":"2026-07-05T10:24:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.04840","created_at":"2026-07-05T10:24:20Z"},{"alias_kind":"pith_short_12","alias_value":"5YY5DO4MJ7YD","created_at":"2026-07-05T10:24:20Z"},{"alias_kind":"pith_short_16","alias_value":"5YY5DO4MJ7YDYGGW","created_at":"2026-07-05T10:24:20Z"},{"alias_kind":"pith_short_8","alias_value":"5YY5DO4M","created_at":"2026-07-05T10:24:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:5YY5DO4MJ7YDYGGWSZYLDMG2VG","target":"record","payload":{"canonical_record":{"source":{"id":"2402.04840","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-02-07T13:41:45Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"264c1986df7219064932c1e76e24282d87f39f44e772465057dc71da6573b9c2","abstract_canon_sha256":"9a296e098d11eb0e62f522f72be383fb807e9ab451fe5c16e7b4587e1459569e"},"schema_version":"1.0"},"canonical_sha256":"ee31d1bb8c4ff03c18d69670b1b0daa9bc1731cc07328b4ea70e625076b16d94","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:24:20.117981Z","signature_b64":"4+eonmdOZJaolgcJVPPa+MCDPlYzr8Ng4quLyoyUL2t/oHZK8UxirXFnCYAV7hMifE+25BdqInAsIGMkYehBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee31d1bb8c4ff03c18d69670b1b0daa9bc1731cc07328b4ea70e625076b16d94","last_reissued_at":"2026-07-05T10:24:20.117240Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:24:20.117240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2402.04840","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:24:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LWERBHq5/IrV2XAJLYDhwCUirIepaGWEiWAO7o8GJC/Qzv9gIwZ70gh+SqWDsLqgryGHpJtnBKgsIYdJKgdLAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T16:45:40.332655Z"},"content_sha256":"81a50fca39cdb17d9afe4c97a39bdbf6f10642d768c2812ae949ef59028a4df1","schema_version":"1.0","event_id":"sha256:81a50fca39cdb17d9afe4c97a39bdbf6f10642d768c2812ae949ef59028a4df1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:5YY5DO4MJ7YDYGGWSZYLDMG2VG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient Estimation of a Gaussian Mean with Local Differential Privacy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Lukas Steinberger, Nikita P. Kalinin","submitted_at":"2024-02-07T13:41:45Z","abstract_excerpt":"In this paper we study the problem of estimating the unknown mean $\\theta$ of a unit variance Gaussian distribution in a locally differentially private (LDP) way. In the high-privacy regime ($\\epsilon\\le 1$), we identify an optimal privacy mechanism that minimizes the variance of the estimator asymptotically. Our main technical contribution is the maximization of the Fisher-Information of the sanitized data with respect to the local privacy mechanism $Q$. We find that the exact solution $Q_{\\theta,\\epsilon}$ of this maximization is the sign mechanism that applies randomized response to the sig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.04840","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.04840/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:24:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Wn6wG5K0+VshigHSuYEl/plrOpL01/tuoXD8iLfx7/y4pX/0/FhH0rF8HfQ58OReOEemL9tS0Xrr7Okps5tCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T16:45:40.333618Z"},"content_sha256":"b5cafb54d92886967e91514bbf43c27938ab30f0e2b068bb7ae13d1c275be7e1","schema_version":"1.0","event_id":"sha256:b5cafb54d92886967e91514bbf43c27938ab30f0e2b068bb7ae13d1c275be7e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5YY5DO4MJ7YDYGGWSZYLDMG2VG/bundle.json","state_url":"https://pith.science/pith/5YY5DO4MJ7YDYGGWSZYLDMG2VG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5YY5DO4MJ7YDYGGWSZYLDMG2VG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-11T16:45:40Z","links":{"resolver":"https://pith.science/pith/5YY5DO4MJ7YDYGGWSZYLDMG2VG","bundle":"https://pith.science/pith/5YY5DO4MJ7YDYGGWSZYLDMG2VG/bundle.json","state":"https://pith.science/pith/5YY5DO4MJ7YDYGGWSZYLDMG2VG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5YY5DO4MJ7YDYGGWSZYLDMG2VG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:5YY5DO4MJ7YDYGGWSZYLDMG2VG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9a296e098d11eb0e62f522f72be383fb807e9ab451fe5c16e7b4587e1459569e","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-02-07T13:41:45Z","title_canon_sha256":"264c1986df7219064932c1e76e24282d87f39f44e772465057dc71da6573b9c2"},"schema_version":"1.0","source":{"id":"2402.04840","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.04840","created_at":"2026-07-05T10:24:20Z"},{"alias_kind":"arxiv_version","alias_value":"2402.04840v3","created_at":"2026-07-05T10:24:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.04840","created_at":"2026-07-05T10:24:20Z"},{"alias_kind":"pith_short_12","alias_value":"5YY5DO4MJ7YD","created_at":"2026-07-05T10:24:20Z"},{"alias_kind":"pith_short_16","alias_value":"5YY5DO4MJ7YDYGGW","created_at":"2026-07-05T10:24:20Z"},{"alias_kind":"pith_short_8","alias_value":"5YY5DO4M","created_at":"2026-07-05T10:24:20Z"}],"graph_snapshots":[{"event_id":"sha256:b5cafb54d92886967e91514bbf43c27938ab30f0e2b068bb7ae13d1c275be7e1","target":"graph","created_at":"2026-07-05T10:24:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2402.04840/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we study the problem of estimating the unknown mean $\\theta$ of a unit variance Gaussian distribution in a locally differentially private (LDP) way. In the high-privacy regime ($\\epsilon\\le 1$), we identify an optimal privacy mechanism that minimizes the variance of the estimator asymptotically. Our main technical contribution is the maximization of the Fisher-Information of the sanitized data with respect to the local privacy mechanism $Q$. We find that the exact solution $Q_{\\theta,\\epsilon}$ of this maximization is the sign mechanism that applies randomized response to the sig","authors_text":"Lukas Steinberger, Nikita P. Kalinin","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-02-07T13:41:45Z","title":"Efficient Estimation of a Gaussian Mean with Local Differential Privacy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.04840","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:81a50fca39cdb17d9afe4c97a39bdbf6f10642d768c2812ae949ef59028a4df1","target":"record","created_at":"2026-07-05T10:24:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9a296e098d11eb0e62f522f72be383fb807e9ab451fe5c16e7b4587e1459569e","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-02-07T13:41:45Z","title_canon_sha256":"264c1986df7219064932c1e76e24282d87f39f44e772465057dc71da6573b9c2"},"schema_version":"1.0","source":{"id":"2402.04840","kind":"arxiv","version":3}},"canonical_sha256":"ee31d1bb8c4ff03c18d69670b1b0daa9bc1731cc07328b4ea70e625076b16d94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee31d1bb8c4ff03c18d69670b1b0daa9bc1731cc07328b4ea70e625076b16d94","first_computed_at":"2026-07-05T10:24:20.117240Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:24:20.117240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4+eonmdOZJaolgcJVPPa+MCDPlYzr8Ng4quLyoyUL2t/oHZK8UxirXFnCYAV7hMifE+25BdqInAsIGMkYehBAg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:24:20.117981Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.04840","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81a50fca39cdb17d9afe4c97a39bdbf6f10642d768c2812ae949ef59028a4df1","sha256:b5cafb54d92886967e91514bbf43c27938ab30f0e2b068bb7ae13d1c275be7e1"],"state_sha256":"c3c1120a91a5f2052de7b3870f31d291919a64b375e4ffa573ed08a7d40714d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gk23u1mr8MhCl6GK1B3UyuZ8g7i5dUO0l+SyxYGwtWEn4xLTWASmBSyyPoB+d0T2TAV0SymQ1EmQC7bscGAaDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T16:45:40.341154Z","bundle_sha256":"66abb51e65330444b15722d9097011c902c29f24955bfdf59263625075cd911c"}}